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Question

limn(n+2)!+(n+1)!(n+2)!(n+1)!


Solution

limn(n+2)!+(n+1)!(n+2)!(n+1)!

Using n!=n(n-1)!

limn(n+2)(n+1)!+(n+1)!(n+2)(n+1)!(n+1)!=limn(n+1)![(n+2)+1](n+1)[(n+2)1]

=limnn+3n+1                       [form]

=limn1+3n1+1n=1+01+0=1

=1

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